A popular heuristic to ensure computational tractability despite the limitations stated above has been to propagate the state covariance () outside the optimizer, based on input and state predictions from the last MPC iteration [1]}, [2]}.
Fixing the covariance matrices \(\Sigma ^x_i\)  at each stage in (REF ) eliminates the corresponding \((n_x + n_x^2)/2\)  augmented states, as well as the need to compute the equality constraint Jacobian derived from (). However, this heuristic generally does not lead to feasible solutions for problem (REF ), as Fig. REF  illustrates.
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